Jani Bergdahl and Bob Bergdahl speak during a news conference in the Rose Garden of the White House on May 31 as President Obama stands by. (Carolyn Kaster/AP)

We've now got a third poll on Bowe Bergdahl, and it's becoming clearer and clearer that this deal is a political dud.

The new CBS News poll shows 45 percent of Americans disapprove of the deal, while 37 percent approve. That's hardly a consensus, of course, and none of the three polls show a majority opposing the deal (yet).

But if you drill down a little deeper on the numbers, you'll see that this situation isn't looking good for the White House.

For a few reasons:

1) Americans wanted to bring Bergdahl home, but not like this

The support that exists for the Bergdahl deal is likely buoyed by the fact that Americans support the general idea of rescuing American prisoners of war. The Pew Research Center poll from Monday showed 55 percent of Americans think POWs should always be rescued, regardless of the circumstances.

That same poll, though, showed only 34 percent thought the deal to trade five Taliban leaders held at Guantanamo Bay for Bergdahl was the right one. In other words, many who thought rescuing Bergdahl was a good idea didn't think this particular deal was a good idea.

The CBS poll also demonstrates this point. While it shows Americans disapproving of the deal 45 percent to 37 percent, when you ask the question a different way, you get a much bigger gap. CBS also asked people whether they thought the price paid was "too high." Well more than half -- 56 percent -- of Americans agree with that statement. Just 28 percent say it was a "reasonable" price.

These two polls both suggest that there are many people who wanted to bring Bergdahl home but think the price was just too steep.

2) A lack of allies

Obama's decision not to notify Congress has rubbed both Congress and the American people the wrong way.

The Obama administration has said that notifying members of Congress about the deal in advance could have jeopardized Bergdahl's safety, but even Democrats like Senate Intelligence Committee Chairwoman Dianne Feinstein (D-Calif.) have suggested that's not a good enough reason to keep someone like her in the dark.

In other words, there is something not to like about this deal for basically everybody involved, including Democratic voters and Democrats in Congress.

What does that mean? It means there probably won't be nearly as many people forcefully defending this deal as forcefully denouncing it. And, as Obamacare has shown, that matters.

3) Veterans hate it

Perhaps the most notable number we've seen so far came from the Pew poll. This poll showed military veterans disapproved of the deal 68 percent to 16 percent, while their families disapproved 55 to 26.

Some have suggested this is merely because members of the military lean conservative. That might be true, but veterans are also the ones most able to relate to this situation and are likely to have the strongest feelings.

So while there's not really a whole lot of people vociferously defending this decision, you're seeing plenty of veterans step forward and emphasize that this was the wrong call. This is a highly sympathetic segment of the population with plenty of strong feelings -- and, again, motivation matters.

4) People care about this issue

This isn't just relevant to veterans and Bowe Bergdahl. The CBS News poll shows 49 percent of Americans say they think the deal will increase the threat of terrorism against the United States. Another 40 percent say it will have no effect, while 3 percent think it will reduce the threat.

If people think this decision emboldened terrorists, that's something that has a potential impact on their own lives.

5) These things tend to get worst before getting better

Right now, opposition to the deal is being driven in large part by the price paid for Bergdahl, but also by reports alleging his desertion and questions about what motivated him to leave his base.

There is a lot of innuendo and rumor right now, and it will probably take a lot of time before we get a clearer picture, because Bergdahl is still recovering and hasn't even spoken to his parents.

In the meantime, though, it's hard to see how questions about Bergdahl will merely disappear and people will feel better about the situation. We would expect support for the deal to stay about where it's at -- if not drop -- as things move forward. Meanwhile, there are about 15 to 20 percent of Americans who are undecided who could really tilt the balance against the Obama administration.

President Obama has professed absolute confidence in the decision that he made, and he might believe that with all his heart, but the American people clearly don't.

That doesn't mean Obama will be seriously damaged, but it does mean that he's at the very least got a public relations problem on his hands.

Aaron Blake covers national politics and writes regularly for The Fix.

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